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History of optics
Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, followed by theories on light and vision developed by ancient Greek and Indian philosophers, and the development of geometrical optics in the Greco-Roman world. The word optics is derived from the Greek term τα ὀπτικά which refers to matters of vision. Optics was significantly reformed by the developments in the medieval Islamic world, such as the beginnings of physical and physiological optics, and then significantly advanced in early modern Europe, where diffractive optics began. These earlier studies on optics are now known as "classical optics". The term "modern optics" refers to areas of optical research that largely developed in the 20th century, such as wave optics and quantum optics. Early history of optics In ancient India, the philosophical schools of Samkhya and Vaisheshika, from around the 6th–5th century BC, developed theories on light. According to the Samkhya school, light is one of the five fundamental "subtle" elements (tanmatra) out of which emerge the gross elements. In contrast, the Vaisheshika school gives an atomic theory of the physical world on the non-atomic ground of ether, space and time. (See Indian atomism.) The basic atoms are those of earth (prthivı), water (apas), fire (tejas), and air (vayu), that should not be confused with the ordinary meaning of these terms. These atoms are taken to form binary molecules that combine further to form larger molecules. Motion is defined in terms of the movement of the physical atoms. Light rays are taken to be a stream of high velocity of tejas (fire) atoms. The particles of light can exhibit different characteristics depending on the speed and the arrangements of the tejas atoms. Around the first century BC, the Vishnu Purana refers to sunlight as the "the seven rays of the sun". In the fifth century BC, Empedocles postulated that everything was composed of four elements; fire, air, earth and water. He believed that Aphrodite made the human eye out of the four elements and that she lit the fire in the eye which shone out from the eye making sight possible. If this were true, then one could see during the night just as well as during the day, so Empedocles postulated an interaction between rays from the eyes and rays from a source such as the sun. In his Optics Greek mathematician Euclid observed that "things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal". In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Ptolemy. In 55 BC, Lucretius, a Roman who carried on the ideas of earlier Greek atomists, wrote: "The light and heat of the sun; these are composed of minute atoms which, when they are shoved off, lose no time in shooting right across the interspace of air in the direction imparted by the shove." —Lucretius , On the nature of the Universe Despite being similar to later particle theories of light, Lucretius's views were not generally accepted and light was still theorized as emanating from the eye. In his Catoptrica, Hero of Alexandria showed by a geometrical method that the actual path taken by a ray of light reflected from a plane mirror is shorter than any other reflected path that might be drawn between the source and point of observation. In a twelfth-century translation assigned to Roman mathematician Claudius Ptolemy, a study of refraction, including atmospheric refraction, was described. It was suggested that the angle of refraction is proportional to the angle of incidence. Later in 499, Aryabhata, who proposed a heliocentric solar system of gravitation in his Aryabhatiya, wrote that the planets and the Moon do not have their own light but reflect the light of the Sun. The Indian Buddhists, such as Dignāga in the 5th century and Dharmakirti in the 7th century, developed a type of atomism that is a philosophy about reality being composed of atomic entities that are momentary flashes of light or energy. They viewed light as being an atomic entity equivalent to energy, similar to the modern concept of photons, though they also viewed all matter as being composed of these light/energy particles. The beginnings of geometrical optics See also: Geometrical optics and Ray (optics) The early writers discussed here treated vision more as a geometrical than as a physical, physiological, or psychological problem. The first known author of a treatise on geometrical optics was the geometer Euclid (c. 325 BC–265 BC). Euclid began his study of optics as he began his study of geometry, with a set of self-evident axioms. 1. Lines (or visual rays) can be drawn in a straight line to the object. 2. Those lines falling upon an object form a cone. 3. Those things upon which the lines fall are seen. 4. Those things seen under a larger angle appear larger. 5. Those things seen by a higher ray, appear higher. 6. Right and left rays appear right and left. 7. Things seen within several angles appear clearer. Euclid did not define the physical nature of these visual rays but, using the principles of geometry, he discussed the effects of perspective and the rounding of things seen at a distance. Where Euclid had limited his analysis to simple direct vision, Hero of Alexandria (c. AD 10–70) extended the principles of geometrical optics to consider problems of reflection (catoptrics). Unlike Euclid, Hero occasionally commented on the physical nature of visual rays, indicating that they proceeded at great speed from the eye to the object seen and were reflected from smooth surfaces but could become trapped in the porosities of unpolished surfaces. This has come to be known as emission theory. Hero demonstrated the equality of the angle of incidence and reflection on the grounds that this is the shortest path from the object to the observer. On this basis, he was able to define the fixed relation between an object and its image in a plane mirror. Specifically, the image appears to be as far behind the mirror as the object really is in front of the mirror. Like Hero, Ptolemy (c. 90–c. 168) considered the visual rays as proceeding from the eye to the object seen, but, unlike Hero, considered that the visual rays were not discrete lines, but formed a continuous cone. Ptolemy extended the study of vision beyond direct and reflected vision; he also studied vision by refracted rays (dioptrics), when we see objects through the interface between two media of different density. He conducted experiments to measure the path of vision when we look from air to water, from air to glass, and from water to glass and tabulated the relationship between the incident and refracted rays. His tabulated results have been studied for the air water interface, and in general the values he obtained reflect the theoretical refraction given by modern theory, but the outliers are distorted to represent Ptolemy's a priori model of the nature of refraction. Optical revolution in the Islamic world Main articles: Physics in medieval Islam and Book of Optics Reproduction of a page of Ibn Sahl's manuscript showing his discovery of the law of refraction, now known as Snell's law. Al-Kindi (c. 801–873) was one of the earliest important optical writers in the Islamic world. In a work known in the west as De radiis stellarum, al-Kindi developed a theory "that everything in the world ... emits rays in every direction, which fill the whole world." This theory of the active power of rays had an influence on later Western scholars such as Robert Grosseteste and Roger Bacon. Ibn Sahl (c. 940-1000) was a Persian mathematician associated with the court of Baghdad. About 984 he wrote a treatise On Burning Mirrors and Lenses in which he set out his understanding of how curved mirrors and lenses bend and focus light. In his work he discovered a law of refraction mathematically equivalent to Snell's law. He used his law of refraction to compute the shapes of lenses and mirrors that focus light at a single point on the axis. edit The beginnings of physical optics Ibn al-Haytham (known in as Alhacen or Alhazen in Western Europe) (965–1040), often regarded as the "father of modern optics", formulated "the first comprehensive and systematic alternative to Greek optical theories." He initiated a revolution in optics and visual perception, also known as the 'Optical Revolution', and laid the foundations for a physical optics. Ibn al-Haytham's key achievement was twofold: first, to insist that vision only occurred because of rays entering the eye and that rays postulated to proceed from the eye had nothing to do with it; the second was to define the physical nature of the rays discussed by earlier geometrical optical writers, considering them as the forms of light and color. He developed a camera obscura to demonstrate that light and color from different candles passed through a single aperture in straight lines, without intermingling at the aperture. He then analyzed these physical rays according to the principles of geometrical optics. Ibn al-Haytham also employed the experimental scientific method as a form of demonstration in optics. He wrote many books on optics, most significantly the Book of Optics (Kitab al Manazir in Arabic), translated into Latin as the De aspectibus or Perspectiva, which disseminated his ideas to Western Europe and had great influence on the later developments of optics. Ibn al-Haytham proved that light travels in straight lines using the scientific method in the Book of Optics. Another aspect associated with Ibn al-Haytham's optical research is related to systemic and methodological reliance on experimentation (i'tibar) and controlled testing in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics ('ilm tabi'i) with mathematics (ta'alim; geometry in particular) in terms of devising the rudiments of what may be designated as a hypothetico-deductive procedure in scientific research. This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae) and grounded his theories of vision, light and color, as well as his research in catoptrics and dioptrics. His legacy was further advanced through the 'reforming' of his Optics by Kamal al-Din al-Farisi (d. ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of al-Haytham's Optics). The Book of Optics established experimentation as the norm of proof in optics, and gave optics a physico-mathematical conception at a much earlier date than the other mathematical disciplines of astronomy and mechanics. The book was influential in both the Islamic world and in Western Europe. Avicenna (980-1037) agreed with Alhazen that the speed of light is finite, as he "observed that if the perception of light is due to the emission of some sort of particles by a luminous source, the speed of light must be finite." Abū Rayhān al-Bīrūnī (973-1048) also agreed that light has a finite speed, and he was the first to discover that the speed of light is much faster than the speed of sound. Abu 'Abd Allah Muhammad ibn Ma'udh, who lived in Al-Andalus during the second half of the 11th century, wrote a work on optics later translated into Latin as Liber de crepisculis, which was mistakenly attributed to Alhazen. This was a "short work containing an estimation of the angle of depression of the sun at the beginning of the morning twilight and at the end of the evening twilight, and an attempt to calculate on the basis of this and other data the height of the atmospheric moisture responsible for the refraction of the sun's rays." Through his experiments, he obtained the value of 18°, which comes close to the modern value. In the late 13th and early 14th centuries, Qutb al-Din al-Shirazi (1236-1311) and his student Kamāl al-Dīn al-Fārisī (1260-1320) continued the work of Ibn al-Haytham, and they were the first to give the correct explanations for the rainbow phenomenon. Al-Fārisī published his findings in his Kitab Tanqih al-Manazir (The Revision of al-Haytham's Optics). In 1574, Taqi al-Din (1526–1585) wrote the last major Arabic work on optics, entitled Kitab Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār (Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights), which contains experimental investigations in three volumes on vision, the light's reflection, and the light's refraction. The book deals with the structure of light, its diffusion and global refraction, and the relation between light and color. In the first volume, he discusses "the nature of light, the source of light, the nature of the propagation of light, the formation of sight, and the effect of light on the eye and sight". In the second volume, he provides "experimental proof of the specular reflection of accidental as well as essential light, a complete formulation of the laws of reflection, and a description of the construction and use of a copper instrument for measuring reflections from plane, spherical, cylindrical, and conical mirrors, whether convex or concave." The third volume "analyses the important question of the variations light undergoes while traveling in media having different densities, i.e. the nature of refracted light, the formation of refraction, the nature of images formed by refracted light." He also describes what may be a rudimentary telescope. The beginnings of physiological optics Ibn al-Haytham discussed the topics of medicine and ophthalmology in the anatomical and physiological portions of the Book of Optics and in his commentaries on Galenic works. He accurately described the process of sight, the structure of the eye, image formation in the eye and the visual system. He also discovered the underlying principles of Hering's law of equal innervation, vertical horopters and binocular disparity, and improved on the theories of binocular vision, motion perception and horopters previously discussed by Aristotle, Euclid and Ptolemy. He discussed ocular anatomy, and was the first author to deal with the "descriptive anatomy" and "functional anatomy" of the eye independently. Much of his descriptive anatomy was faithful to Galen's gross anatomy, but with significant differences in his approach. For example, the whole area of the eye behind the iris constitutes what Ibn al-Haytham uniquely called the uveal sphere, and his description of the eye was devoid of any teleological or humoral theories associated with Galenic anatomy. He also described the eye as being made up of two intersecting globes, which was essential to his functional anatomy of the eye. After describing the construction of the eye, Ibn al-Haytham makes his most original anatomical contribution in describing the functional anatomy of the eye as an optical system, or optical instrument. His multiple light-source experiment via a reduction slit with the camera obscura, also known as the lamp experiment, provided sufficient empirical grounds for him to develop his theory of corresponding point projection of light from the surface of an object to form an image on a screen. It was his comparison between the eye and the beam-chamber, or camera obscura, which brought about his synthesis of anatomy and optics, giving rise to a new field of optics now known as "physiological optics". As he conceptualized the essential principles of pinhole projection from his experiments with the pinhole camera, he considered image inversion to also occur in the eye, and viewed the pupil as being similar to an aperture. Regarding the process of image formation, however, he incorrectly agreed with Avicenna that the lens was the receptive organ of sight, but correctly hinted at the retina also being involved in the process. Optics in medieval Europe The English bishop, Robert Grosseteste (c. 1175–1253), wrote on a wide range of scientific topics at the time of the origin of the medieval university and the recovery of the works of Aristotle. Grosseteste reflected a period of transition between the Platonism of early medieval learning and the new Aristotelianism, hence he tended to apply mathematics and the Platonic metaphor of light in many of his writings. He has been credited with discussing light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology or physics of light, and a theology of light. Setting aside the issues of epistemology and theology, Grosseteste's cosmogony of light describes the origin of the universe in what may loosely be described as a medieval "big bang" theory. Both his biblical commentary, the Hexaemeron (1230 x 35), and his scientific On Light (1235 x 40), took their inspiration from Genesis 1:3, "God said, let there be light", and described the subsequent process of creation as a natural physical process arising from the generative power of an expanding (and contracting) sphere of light. Optical diagram showing light being refracted by a spherical glass container full of water. (from Roger Bacon or Robert Grosseteste) His more general consideration of light as a primary agent of physical causation appears in his On Lines, Angles, and Figures where he asserts that "a natural agent propagates its power from itself to the recipient" and in On the Nature of Places where he notes that "every natural action is varied in strength and weakness through variation of lines, angles and figures." The English Franciscan, Roger Bacon (c. 1214–1294) was strongly influenced by Grosseteste's writings on the importance of light. In his optical writings (the Perspectiva, the De multiplicatione specierum, and the De speculis comburentibus) he cited a wide range of recently translated optical and philosophical works, including those of Alhacen, Aristotle, Avicenna, Averroes, Euclid, al-Kindi, Ptolemy, Tideus, and Constantine the African. Although he was not a slavish imitator, he drew his mathematical analysis of light and vision from the writings of the Arabic writer, Alhacen. But he added to this the Neoplatonic concept, perhaps drawn from Grosseteste, that every object radiates a power (species) by which it acts upon nearby objects suited to receive those species. Note that Bacon's optical use of the term "species" differs significantly from the genus / species categories found in Aristotelian philosophy. Another English Franciscan, John Pecham (died 1292) built on the work of Bacon, Grosseteste, and a diverse range of earlier writers to produce what became the most widely used textbook on Optics of the Middle Ages, the Perspectiva communis. His book centered on the question of vision, on how we see, rather than on the nature of light and color. Pecham followed the model set forth by Alhacen, but interpreted Alhacen's ideas in the manner of Roger Bacon. Like his predecessors, Witelo (c. 1230–1280 x 1314) drew on the extensive body of optical works recently translated from Greek and Arabic to produce a massive presentation of the subject entitled the Perspectiva. His theory of vision follows Alhacen and he does not consider Bacon's concept of species, although passages in his work demonstrate that he was influenced by Bacon's ideas. Judging from the number of surviving manuscripts, his work was not as influential as those of Pecham and Bacon, yet his importance, and that of Pecham, grew with the invention of printing. * Peter of Limoges (1240–1306) * Theodoric of Freiberg (ca. 1250–ca. 1310) Renaissance and early modern optics Johannes Kepler (1571–1630) picked up the investigation of the laws of optics from his lunar essay of 1600. Both lunar and solar eclipses presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse. Related issues of atmospheric refraction applied to all astronomical observations. Through most of 1603, Kepler paused his other work to focus on optical theory; the resulting manuscript, presented to the emperor on January 1, 1604, was published as Astronomiae Pars Optica (The Optical Part of Astronomy). In it, Kepler described the inverse-square law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole cameras, as well as the astronomical implications of optics such as parallax and the apparent sizes of heavenly bodies. Astronomiae Pars Optica is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent). Willebrord Snellius (1580–1626) found the mathematical law of refraction, now known as Snell's law, in 1621. Subsequently René Descartes (1596–1650) showed, by using geometric construction and the law of refraction (also known as Descartes' law), that the angular radius of a rainbow is 42° (i.e. the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's center is 42°). He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law. Christiaan Huygens (1629–1695) wrote several works in the area of optics. These included the Opera reliqua (also known as Christiani Hugenii Zuilichemii, dum viveret Zelhemii toparchae, opuscula posthuma) and the Traitbe de la lumiaere. Isaac Newton (1643–1727) investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colors, and that a lens and a second prism could recompose the multicolored spectrum into white light. He also showed that the colored light does not change its properties by separating out a colored beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same color. Thus, he observed that color is the result of objects interacting with already-colored light rather than objects generating the color themselves. This is known as Newton's theory of color. From this work he concluded that any refracting telescope would suffer from the dispersion of light into colors, and invented a reflecting telescope (today known as a Newtonian telescope) to bypass that problem. By grinding his own mirrors, using Newton's rings to judge the quality of the optics for his telescopes, he was able to produce a superior instrument to the refracting telescope, due primarily to the wider diameter of the mirror. In 1671 the Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes On Color, which he later expanded into his Opticks. Newton argued that light is composed of particles or corpuscles and were refracted by accelerating toward the denser medium, but he had to associate them with waves to explain the diffraction of light (Opticks Bk. II, Props. XII-L). Later physicists instead favoured a purely wavelike explanation of light to account for diffraction. Today's quantum mechanics, photons and the idea of wave-particle duality bear only a minor resemblance to Newton's understanding of light. In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. In 1704, Newton published Opticks, in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation "Are not gross Bodies and Light convertible into one another, ...and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?" The beginnings of diffraction optics Thomas Young's sketch of two-slit diffraction, which he presented to the Royal Society in 1803 The effects of diffraction of light were first carefully observed and characterized by Francesco Maria Grimaldi, who also coined the term diffraction, from the Latin diffringere, 'to break into pieces', referring to light breaking up into different directions. The results of Grimaldi's observations were published posthumously in 1665.5354 Isaac Newton studied these effects and attributed them to inflexion of light rays. James Gregory (1638–1675) observed the diffraction patterns caused by a bird feather, which was effectively the first diffraction grating. In 1803 Thomas Young did his famous experiment observing interference from two closely spaced slits. Explaining his results by interference of the waves emanating from the two different slits, he deduced that light must propagate as waves. Augustin-Jean Fresnel did more definitive studies and calculations of diffraction, published in 1815 and 1818, and thereby gave great support to the wave theory of light that had been advanced by Christian Huygens and reinvigorated by Young, against Newton's particle theory. Lenses and lensmaking See also: Timeline of telescope technology The earliest known lenses were made from polished crystal, often quartz, and have been dated as early as 700 BC for Assyrian lenses such as the Layard / Nimrud lens. There are many similar lenses from ancient Egypt, Greece and Babylon. The ancient Romans and Greeks filled glass spheres with water to make lenses. Glass lenses were not thought of until the Middle Ages. Ibn al-Haytham (Alhacen) wrote about the effects of pinhole and concave lenses in his Book of Optics,5556 which was influential in the development of the modern telescope. The earliest evidence of "a magnifying device, a convex lens forming a magnified image," also dates back to his Book of Optics. Roger Bacon used parts of glass spheres as magnifying glasses and recommended them to be used to help people read. Roger Bacon got his inspiration from Alhacen in the 11th century. He discovered that light reflects from objects and does not get released from them. Around 1284 in Italy, Salvino D'Armate is credited with inventing the first wearable eye glasses. Between the 11th and 13th century "reading stones" were invented. Often used by monks to assist in illuminating manuscripts, these were primitive plano-convex lenses initially made by cutting a glass sphere in half. As the stones were experimented with, it was slowly understood that shallower lenses magnified more effectively. There is some documentary evidence, but no surviving designs or physical evidence, that the principles of telescopes were known in the late 16th century. Leonard Digges, Taqi al-Din and Giambattista della Porta61 independently developed rudimentary telescopes in the 1570s and 1580s. However, the earliest known working telescopes were the refracting telescopes that appeared in the Netherlands in 1608. Their development is credited to three individuals: Hans Lippershey and Zacharias Janssen, who were spectacle makers in Middelburg, and Jacob Metius of Alkmaar. Galileo greatly improved upon these designs the following year. Isaac Newton is credited with constructing the first functional reflecting telescope in 1668, his Newtonian reflector. The first microscope was made around 1595 in Middleburg, Holland. Three different eyeglass makers have been given credit for the invention: Hans Lippershey (who also developed the first real telescope); Hans Janssen; and his son, Zacharias. The coining of the name "microscope" has been credited to Giovanni Faber, who gave that name to Galileo Galilei's compound microscope in 1625. Quantum optics Main article: Quantum optics Light is made up of particles called photons and hence inherently is quantized. Quantum optics is the study of the nature and effects of light as quantized photons. The first indication that light might be quantized came from Max Planck in 1899 when he correctly modeled black-body radiation by assuming that the exchange of energy between light and matter only occurred in discrete amounts he called quanta. It was unknown whether the source of this discreteness was the matter or the light. In 1905, Albert Einstein published the theory of the photoelectric effect. It appeared that the only possible explanation for the effect was the quantization of light itself. Later, Niels Bohr showed that atoms could only emit discrete amounts of energy. The understanding of the interaction between light and matter following from these developments not only formed the basis of quantum optics but also were crucial for the development of quantum mechanics as a whole. However, the sub fields of quantum mechanics dealing with matter-light interaction were principally regarded as research into matter rather than into light and hence, one rather spoke of atom physics and quantum electronics. This changed with the invention of the maser in 1953 and the laser in 1960. Laser science—research into principles, design and application of these devices—became an important field, and the quantum mechanics underlying the laser's principles was studied now with more emphasis on the properties of light, and the name quantum optics became customary. As laser science needed good theoretical foundations, and also because research into these soon proved very fruitful, interest in quantum optics rose. Following the work of Dirac in quantum field theory, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light (see degree of coherence). This led to the introduction of the coherent state as a quantum description of laser light and the realization that some states of light could not be described with classical waves. In 1977, Kimble et al. demonstrated the first source of light which required a quantum description: a single atom that emitted one photon at a time. Another quantum state of light with certain advantages over any classical state, squeezed light, was soon proposed. At the same time, development of short and ultrashort laser pulses—created by Q-switching and mode-locking techniques—opened the way to the study of unimaginably fast ("ultrafast") processes. Applications for solid state research (e.g. Raman spectroscopy) were found, and mechanical forces of light on matter were studied. The latter led to levitating and positioning clouds of atoms or even small biological samples in an optical trap or optical tweezers by laser beam. This, along with Doppler cooling was the crucial technology needed to achieve the celebrated Bose-Einstein condensation. Other remarkable results are the demonstration of quantum entanglement, quantum teleportation, and (recently, in 1995) quantum logic gates. The latter are of much interest in quantum information theory, a subject which partly emerged from quantum optics, partly from theoretical computer science. Today's fields of interest among quantum optics researchers include parametric down-conversion, parametric oscillation, even shorter (attosecond) light pulses, use of quantum optics for quantum information, manipulation of single atoms, Bose-Einstein condensates, their application, and how to manipulate them (a sub-field often called atom optics), and much more. Research into quantum optics that aims to bring photons into use for information transfer and computation is now often called photonics to emphasize the claim that photons and photonics will take the role that electrons and electronics now have. Category:Optics